An undirected graph \(G=(V,A)\) by a set V of n nodes, a set A of m edges, and two sets \(S,\ D\subseteq V\) consists of source and demand nodes are given. This paper presents two new versions of location problems which are called the \(f(\sigma )\)-location and \(g(\sigma )\)-location problems. We define an \(f(\sigma )\)-location of the network N as a node \(s\in S\) with the property that the maximum expense transmission time from the node s to the destinations of D is as cheap as possible. The \(f(\sigma )\)-location problem divides the range \((0,\infty )\) into intervals \(\displaystyle \cup _{i}{(a_i,b_i)}\) and finds a source \(s_i\in S\), for each interval \((a_i,b_i)\), such that \(s_i\) is a \(f(\sigma )\)-location for each \(\sigma \in (a_i,b_i)\). Also, define a \(g(\sigma )\)-location as a node s of S with the property that the sum of expense transmission times from the node s to all destinations of D is as cheap as possible. The \(g(\sigma )\)-location problem divides the range \((0,\infty )\) into intervals \(\displaystyle \cup _{i}{(a_i,b_i)}\) and finds a source \(s_i\in S\), for each interval \((a_i,b_i)\), such that \(s_i\) is a \(g(\sigma )\)-location for each \(\sigma \in (a_i,b_i)\). This paper presents two strongly polynomial time algorithms to solve \(f(\sigma )\)-location and \(g(\sigma )\)-location problems.

由n 个节点的集合V 、 m 个边的集合A以及由源节点和需求节点组成的两个集合\(S,\ D\subseteq V\) 组成的无向图\(G=(V,A) \)为给予。本文提出了两个新版本的位置问题，称为\(f(\sigma )\)位置问题和\(g(\sigma )\)位置问题。我们将网络N的f(sigma )位置定义为节点s in S ，其属性是从节点s到D的目的地的最大费用传输时间是便宜的尽可能。 \ (f(\sigma )\)位置问题将范围\((0,\infty )\)划分为区间\(\displaystyle \cup _{i}{(a_i,b_i)}\)并找到一个源\(s_i\in S\)，对于每个间隔\((a_i,b_i)\)，使得\(s_i\)是每个\( \sigma \) 的\(f(\sigma )\)位置在 (a_i,b_i)\) 中。另外，将g(sigma )位置定义为S的节点s ，其属性是从节点s到D的所有目的地的费用传输时间之和尽可能便宜。 \ (g(\sigma )\)位置问题将范围\((0,\infty )\)划分为区间\(\displaystyle \cup _{i}{(a_i,b_i)}\)并找到一个源\(s_i\in S\)，对于每个间隔\((a_i,b_i)\)，使得\(s_i\)是每个\( \sigma \) 的\(g(\sigma )\)位置在 (a_i,b_i)\) 中。本文提出了两种强多项式时间算法来解决\(f(\sigma )\)位置和\(g(\sigma )\)位置问题。